Spectral boundary conditions in one-loop quantum cosmology

Journal Article · Sun Sep 15 00:00:00 EDT 1991 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.44.1713· OSTI ID:5182809

D'Eath, P D ^[1]; Esposito, G V.M. ^[2]

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1. Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW (United Kingdom)
2. Department of Applied Mathematics and Theorectical Physics, Silver Street, Cambridge CB3 9EW (United Kingdom) St. John's College, Cambridge CB2 1TP (United Kingdom)

For fermionic fields on a compact Riemannian manifold with a boundary, one has a choice between local and nonlocal (spectral) boundary conditions. The one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be studied using the generalized Riemann {zeta} function formed from the squared eigenvalues of the four-dimensional fermionic operators. For a massless Majorana spin-1/2 field, the spectral conditions involve setting to zero half of the fermionic field on the boundary, corresponding to harmonics of the intrinsic three-dimensional Dirac operator on the boundary with positive eigenvalues. Remarkably, a detailed calculation for the case of a flat background bounded by a three-sphere yields the same value {zeta}(0)=11/360 as was found previously by the authors using local boundary conditions. A similar calculation for a spin-3/2 field, working only with physical degrees of freedom (and, hence, excluding gauge and ghost modes, which contribute to the full Becchi-Rouet-Stora-Tyutin-invariant amplitude), again gives a value {zeta}(0)={minus}289/360 equal to that for the natural local boundary conditions.

• OSTI ID: 5182809
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 44:6; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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